Lab 1

function [sum] = vecsum(RV)
%this function will input a row vector and return a sum of all the elements
L = length(RV);
i = 1;
sum = 0;
while i <= L
    sum = sum + RV(i);
    i = i + 1;
end
end

function [A,B,dA,dB] = wregression(x,y,dy)
%this function calculates slope, y intercept and uncertainty in both
%it also assumes that x, y and dy are of the same length
w = 1./(dy.^2);
%First we get the sums we will need to find our return values
w_sum = vecsum(w);
wy_sum = vecsum(w.*y);
wx_sum = vecsum(w.*x);
wxy_sum = vecsum(w.*x.*y);
wx2_sum = vecsum(w.*(x.^2));
%Now we find the value of D to be used later
D = (w_sum*wx2_sum) - (wx_sum^2);
%Here we use our sums along with D to find the return values
A = ((wx2_sum*wy_sum)-(wx_sum*wxy_sum))/D;
B = ((w_sum*wxy_sum)-(wx_sum*wy_sum))/D;
dA = sqrt(wx2_sum/D);
dB = sqrt(w_sum/D);
end

function regressionplot(x,y,dy)
hold on
figure(1)
errorbar(x,y,dy,'rx')
xfit = linspace(0,5);
[A,B,dA,dB] = wregression(x,y,dy);
yfit = xfit*B + A;
plot(xfit,yfit)
end

function [z2] = zSq(V,I);
z2 = (V./I).^2;
end

function [R L dR dL] = indRes(f,V,I,dV,dI)
f=[152 361 568 823 1031 1358]; % frequency [Hz];
V=[1.63 2.01 2.47 3.00 3.34 3.75]; % inductor RMS voltage [V]
I=[0.0615 0.0593 0.056 0.0512 0.0472 0.0413]; % inductor RMS current [A]
dV=V*0.005+0.02; % Uncertainty in the voltage measurements [V]
dI=I*0.0075+0.0002; % Uncertainty in the current measurements [A]
radF = (2*f*pi).^2;
z2 = zSq(V,I);
dZSq=((zSq(V+dV,I)-zSq(V,I)).^2+(zSq(V,I+dI)-zSq(V,I)).^2).^0.5;
[R2,L2,dR2,dL2] = wregression(radF,z2,dZSq);
R = R2^0.5;
L = L2^0.5;
dR = abs((R2+dR2)^0.5 - (R2)^0.5);
dL = abs((L2+dL2)^0.5 - (L2)^0.5);
end

function [A B dA dB] = capa(f,V,I,dV,dI)
f=[113 124 212 238 294 350 395 489]; % frequency [Hz]
V=[7.39 7.47 7.46 7.35 7.36 7.35 7.44 7.43]; % Capacitor RMS Voltage [V]
I=[2.51 2.73 4.82 5.41 6.61 7.81 8.91 11.2]*10^-3; % RMS Current [A]
dV=V*0.005+0.02; % Experimental Uncertainty in Voltage Measurements [V]
dI=I*0.0075+0.0002; % Uncertainty in Current [A]
radF = (2*f*pi).^2;
xvals = 1./radF
z2 = zSq(V,I);
dZSq=((zSq(V+dV,I)-zSq(V,I)).^2+(zSq(V,I+dI)-zSq(V,I)).^2).^0.5;
[R2,cap2,dR2,dCap2] = wregression(xvals,z2,dZSq);
R = R2^0.5;
cap = cap2^-0.5;
dR2 = abs((R2+dR2)^0.5 - (R2)^0.5);
dCap2 = abs((1/(cap2+dCap2))^0.5 - (1/cap2)^0.5);
end